I've read David Cordingley's 'Cochrane the Dauntless", Arthur Herman's 'To Rule the Waves', and begun the Aubrey-Maturin fiction series and all three mention officers being stuck ashore on half-pay.
What did these officers tend to do when not on a seagoing vessel? Did they get given postings ashore like the modern Navy doing administrative work or logistic support or were they effectively on a half-paid form of leave?
The concept of officers being put ashore on half pay was an integral part of the management of the British Army and Royal Navy of the 18th, 19th and early 20th centuries. Half-Pay referred to the pay an officer received when in retirement or when not in actual service. Thus, it could have been given either for full retirement (for age, disability, etc.), or as a result of a reduction in force (RIF). During periods when the Royal Navy, for example, was decreasing in size, there were more trained and experienced officers available than billets for them. Thus, the excess officers were essentially discharged temporarily on half pay, with no guarantee that they would ever be recalled to full active duty in the future (hopefully when the size of the RN again grew large enough to provide sea-going billets for them). So, in direct answer to your question, it was effectively on a half-paid form of long term leave (which might not end until their deaths), or temporary retirement.
Your last clause has it right -- half-pay was thought of as a retainer for future employment of officers, as a way of keeping them officially in the Navy rather than looking for other employment. Keep in mind that during the entire period of the Napoleonic wars well up into the mid-19th century, there was no form of regularized enlistment for sailors -- they were attached to a ship for a commission, paid off at the end and that was it. Officers were in much the same place until the late 1600s. It wasn't until 1691 that the RN had a regularized seniority list of officers (that is, a list of all the officers in the navy, in one place, including who's senior to the other). Half-pay was introduced in 1694 and was clarified in 1713 as a system to grant it to captains and lieutenants who "stand fair to be employed when there will be an occasion" (N.A.M. Rodger, Command of the Ocean, pp. 203).
I wrote more about pay, conscription, promotion and manning in these answers if it's of interest here:
and here: